Basic
Development and Decision Processes:
Technical and Economic Analyses
Michael
Tekletsion Berhan
African Technology Forum
Copyright
2000
Published
on-line at:
www.africantechnologyforum.org
and
http://africantech.home.att.net/home.htm
As mentioned in the introduction, here is a very basic introduction of general financial criteria and figures of merit that can be used directly in the decision matrices mentioned herein to help select between competing developments and investments. While the level of detail presented here will be well below the level of the experienced financial professional, the beginner or the development professional who has not been exposed to these analyses will most likely benefit.
For further discussion, refer to economic textbooks such as Don Merino and Hans Lang's The Selection Process for Capital Projects, or an experienced financial analyst who can go into detail about the nuances of using these analyses to make decisions for any particular project. Basic micro- and macro-economic concepts that describe the workings and environment of any financial venture can be learned from a study of Nobel laureate Paul Samuelson's classic text Economics. African Technology Forum Consulting may be contacted to provide detailed examples of how to apply these calculations to a particular situation. Write to us at africantech@att.net, mtberhan@alum.mit.edu, or mtberhan@att.net for any such assistance.. As of December 2000, you may visit www.teachmefinance.com as another quick reference for these topics and their related financial calculations.
The "time value of money" is the fiscal value of a given amount of money with respect to time, based on a particular interest rate, or "rate of return", over that period of time. There are two basic types of interest rates used, "simple" and "compound". They differ in how the monetary value changes, arithmetically or exponentially. For long-term projects, the difference can be staggering.
The formula for determining the value of an amount of money that is subject to a simple interest rate is as follows: F = P * (1 + i * N), where P = the given amount of money or "principal", i = the interest rate, N = the periods of time in question, and F = the value after those periods are over. What this says is that for a financial amount where the rate of return i is given per period for N periods, the value grows by N amounts of i percentage. Hence, if a Nigerian business borrows 1,000,000 naira from an international funding source that only requires a simple rate of return of 4% per annum be paid, the business owes that source a total of 1,000,000 * (1 + 0.04) = 1,040,000 naira after the first year of the loan. It would owe 1,000,000 * (1 + 0.04 * 2) = 1,080,000 after the second year, and an additional 40,000 naira each subsequent year. The time value of that loan, after ten years, not accounting for currency fluctuations and/or inflation, would be 1,000,000 * (1 + 0.04 * 10) = 1,400,000 naira.
For an amount of money that is subject to a compound interest rate, the formula is F = P * (1 + i) ^ N. Compounding denotes geometric growth. If the same business had to pay back the same loan using a numerically lower interest rate of 3.5%, yet it was to be compounded annually, after the first year the business owes 1,000,000 * (1 + 0.035) ^ 1 = 1,035,000 naira. After the second year, the value of the loan is 1,000,000 * (1 + 0.035) ^ 2 = 1,035,000 * 1.035 = 1,071,225 naira. For now, this is still less than with the 4% simple rate from before. After ten years, however, the value of the compounded loan is 1,000,000 * (1 + 0.035) ^ 10 = 1,410,599 naira. The scaling power of the smaller numeric rate has been overtaken by the increased frequency by which it is implemented. With compounding's exponential growth, the rate affects not only the original principal amount, but builds on previous growth. The second year valuation reflects a change in the first year's valuation, the third year's the second, and so on. If the two loans were to be compared over a thirty year period, the valuation of the simple rate of return loan would be 1,000,000 * (1 + 0.04 * 30) = 2,200,000 naira, whereas the compound rate of return loan would be valued at 1,000,000 * (1 + 0.035) ^ 30 = 2,806,749 naira. If both loans were at a 4% rate, the 30-year compound loan would be valued at 1,000,000 * (1 + 0.04) ^ 30 = 3,243,398 naira.
Compounding rates of return are the most common, both for loans and investments, and in natural economic situations, such as inflation. An inflation rate, unfortunately, does not minimize its damage by growing in linear, additive steps. It is a geometric phenomenon. In a second year, it builds on the damage it did in the first year, and in the third year, it builds on the larger damage it did in the second year. At 3.5% inflation, a product that costs 1,000,000 naira in the first year will cost 1,071,225 naira in two years. This is a major reason why simple rates of return are so rare to find in loans outside of charity cases and a few programs for impoverished nations. The lender has to make sure their loan, at a minimum, has to outpace the compounding inflation they themselves face. A for-profit lender wants to make sure that the amount of money it is releasing control of now will come back to it with a greater overall value in the future. Without a beneficial time value of money for the loan, it has no reason at all to make the loan. The lender can do better for itself by investing elsewhere right now.
There are two sub-sets of compounding rates of return, nominal interest rates and effective interest rates. These delineate how the compounding period is calculated. Nominal interest rates are equivalent to a given periodic rate multiplied by the number of compounding periods per year. Thus, if the rate is 1% per month, the nominal rate is 1% * 12 = 12% per annum. Nominal rates are usually taken to mean annually compounding rates of return. If the periodic rate is quoted at 2% per quarter, the nominal rate is 2% * 4 = 8% annually. This does not mean, however, that the actual annual rate of return is the same as the nominal rate.
If the rate is to compound at multiple periods per year, an effective annual interest rate can be determined by (1 + iperiodic) ^ nperiods - 1. The effective rate for twelve months of 1% per month compounding monthly rather than at the end of the year is (1 + 0.01) ^ 12 - 1 = 12.68%, which is a bit higher than the nominal rate. An effective annual rate for 2% quarterly compounding is (1 + 0.02) ^ 4 - 1 = 8.24%; again, higher than the nominal rate. Sometimes, the effective rate is called the yield, since it denotes what the compounding yields in practical terms. Thus, a loan with a nominal interest rate of 8% has an annual yield of 8.24% if it compounds at a periodic rate of 2% per quarter.
A specific type of compounding rate used to generate an effective yield is the continuous compounding rate. Here, the span of each compounding period is considered to be infinitely small. An effective annual rate under continuous compounding is calculated exponentially. The formula is iannual = e ^ inominal - 1. Thus, for a nominal rate of 15%, if compounded continuously, the effective annual rate is e ^ 0.15 - 1 = 1.1618 - 1 = 16.18%. Note that while continuous compounding can sound difficult and problematic for the debtor due to its exponential nature, it is not much greater than monthly or daily compounding for most practical investment lifespans. If the 15% nominal rate was compounded monthly, it would yield an effective annual rate of (1 + (0.15 / 12)) ^ 12 - 1 = 16.08%. If it were compounded daily, the effective annual rate would be (1 + (0.15 / 365)) ^ 365 - 1 = 16.1798%; for all intents and purposes the same as the continuous rate's result. While continuous compounding may not be used as commonly in loans or in investment situations in developing countries, it is not uncommon in developed countries. Thus, developers and decision makers who are competing for investment money on the open market need to at least be aware that it exists. It is another form of compounding that their audience can turn to if they do not provide an attractive enough rate of return themselves.
Minimum Attractive Rate of Return (MARR) and Payback Period
One of the most important concepts in economic analysis is the minimum attractive rate of return. The minimum attractive rate of return (MARR) is the lowest rate of return that investors will accept before they invest in light of the investment risk (which is always present) or the opportunity to invest elsewhere for possibly greater returns. MARR is related in a time sense to the payback period. The payback period is that time which it takes an investment to pay the investors back a particular outlay (such as their initial investment), after which, they are taking in more than they put out. As mentioned above, at a minimum an investment should outpace the inflation rate the investor faces, or in all reality it is a money-losing venture. For-profit investors tend to look at investments in one of two ways: will this investment pay back a net rate of return that is greater than some minimum acceptable rate, or will it pay back a net profit before some maximum length of payback period? MARR has an inverse relationship to the payback period. The smaller the acceptable rate of return, the longer an investor is willing to wait to see a net profit. The higher the rate of return, the shorter the time the investor is willing to wait to see a profit returned to them. However, MARR is a compounding fiscal value, whereas payback period does not directly take into account how the value of the investment itself has changed over time. MARRs are usually quoted as effective annual rates.
Because of the threat, real or imagined, of risk to their investment in a given socio-economic or political environment, most for-profit investors look for a higher MARR in developing areas and regions than they do in established, stable regions. A businesswoman will choose to keep her $1,000,000 USD in New York if she knows she can at a minimum make 6% annual profit in guaranteed investments there, rather than invest it in a politically unstable nation even if she can probably make 6% there as well. Her MARR for an American investment is 6% or lower, but is greater than 6% for a supposedly riskier market. Even with the leverage that larger, multi-national companies almost always have even in regions that are new to them, they usually require a larger estimated rate of return in the newer region than they do in their home markets. For example, an electronic products company that may require an estimated rate of return of 10% for an investment in a new factory in Paris might not even bother entertaining a proposal to build the same operation in a politically unstable former French colony unless it estimates it could see an annual return of 20%.
While increases in MARR tend to be judged market by market, some companies set an internal policy of across-the-board MARR increase for any foreign market, especially in a least developed country. This often results in a flat rate increase in their MARR for "stable" economy markets of 2-5% above that for the home market, and 5-20% or greater for investments in LDCs.
In economics, a "figure of merit" means a numeric metric used to judge the value of an investment or financial operation. A metric like payback period is one type of figure of merit, as it can be used to judge an investment. The most common figures of merit are ratios and rates of return.
Return on Investment (ROI) is a common, yet overly simplistic metric used that too often ignores the time value of money used in the investment. ROI in its basic form is calculated as net income divided by investment sum. This is fine if the investment is only looked at for one year, but for beyond a single year, compounding over that time is ignored and the picture is distorted. Average ROI is sometimes used, where the ROI is average net annual income divided by original investment. This too ignores the time value of that money involved, but as a simple "snapshot" metric it can be used to quickly compare several different investment options at once.
For projects where the investments have a residual "salvage" value after a given lifespan of service, Return on Average Investment (ROAI) can be used instead of ROI. This is more common in simple analyses of plant, property, and equipment purchases. ROAI is average net income divided by the average book value of the investment. If a new industrial generator in Benin can be purchased for 1,000,000 CFA francs and then re-sold in working condition for CFA 300,000 six years later, the average book value of that investment is CFA 650,000. Assuming the generator allows for an additional net income of CFA 120,000 per year, the ROI = 120,000 / 1,000,000 = 12% whereas the ROAI = 120,000 / 650,000 = 18.46%. Compounding, however, is as absent from basic ROAI analyses as it is from the basic ROI calculations above, so they all should only be used as "snapshots". In this example, for instance, six years can obviously make a huge difference in the time value of money.
To properly account for the time value of money in a decision process, we need to use discounted figures of merit. These directly take into account how the monetary value of the investment itself has changed over time. First, let us define "discounting", which despite its name does not have a negative connotation. Discounting is simply the process of calculating what value a future sum of money would have at an earlier time, at a given rate of compounding. For instance, if an Ethiopian businessman wants to have 200,000 birr before tax for a purchase in five years, and can invest now overseas at a guaranteed effective annual rate of 6%, how much does he need to set aside, inflation notwithstanding? This is solved as the inverse of compounding, (1 + iperiodic) ^ -nperiods. Thus, the businessman presently needs to invest 200,000 * (1 + 0.06) ^ -5 = 200,000 / ((1.06) ^ 5) = 149, 452 birr.
Some of the most basic yet important time value, or discounted, economic figures of merit are:
These are all ways to measure the time value of money for any given investment, real or analytical, large or small, past, present, or future. (Note that the terms "worth" and "value" are interchangeable in this context. This is common in economic analyses.) Let's go over how these are all calculated.
The present worth (PW) of a future amount is what its monetary value is at this moment. The value of the 200,000 birr in five years is the same to the Ethiopian businessman above as the 149,452 birr is today if he can get that 6% effective annual yield. PW for a given for-profit investment is calculated using the MARR that the investor has chosen to proceed at. For non-profit investments and loans, it can be reduced to the estimated rate of inflation that the project will witness over its lifespan.
Where there are multiple cash flows over a project's life, a net present worth (NPW) can be calculated. Let us revisit the Beninois business that is looking to purchase the generator and run the operation for those six years. They would pay 1,000,000 CFA francs right now for the generator. If they were lucky enough to pay a fixed price for gasoline and the raw materials for their product and it cost them CFA 30,000 per year, yet their additional revenues from this operation stayed flat at CFA 150,000, we would have the same annual net income as before, CFA 120,000. Now, what if they have selected a MARR of 12%? What would the NPW of this investment be?
The PW at day one equals the cost of the generator, CFA 1,000,000. The estimated PW of the net income over those six years is
PWin = 120,000 * (1 + 0.12) ^ -6 + 120,000
* (1 + 0.12) ^ -5 + 120,000 * (1 + 0.12) ^ -4
+ 120,000 * (1 + 0.12) ^ -3 + 120,000 * (1 + 0.12) ^ -2 + 120,000 * (1 +
0.12) ^ -1
= 120,000 * [0.5066 + 0.5674 + 0.6355 + 0.7118 +
0.7972 + 0.8929] = 120,000 * 4.1114
= CFA 493,369
Thus, the net present worth of the investment is 493,369 - 1,000,000 = CFA -506,631. Clearly, the operation as envisioned in this stage is not a viable for-profit investment option. Even if the generator could be re-sold for CFA 300,000 at the end of the six years, the actual present time value of their salvage would be 300,000 * (1 + 0.12) ^ -6 = 300,000 * 0.5066 = CFA 151,989. The overall PWin would only be 493,369 + 151,989 = CFA 645,358. The NPW would still be an estimated loss at 645,358 - 1,000,000 = CFA -354,642.
Either the operation would have to run for well more than six years, the net annual income generated would have to be higher, or the businesspeople involved would have to live with a MARR below 12%. If the acceptable rate of return was reduced to 5%, the purchase price of the generator was negotiated down to CFA 800,000, and the businesspeople still believe the generator could be re-sold for CFA 300,000 at the end of year six, then the NPW of the investment would be a positive CFA 32,948. A positive NPW, however small, means that the investment as estimated should return more than the MARR. Being forced from an MARR of 12% to 5% might mean, however, that the operation planned here no longer suits the investors' needs, as such a reduction might not truly be "minimally acceptable". Note that the previously considered basic ROI and basic ROAI analyses would have been useless in judging the true value of this particular investment option under either scenario.
When the cash flows for an operation have a uniform flow of steady payments, or "annuities", rather than just a few payments, a discounted uniform series or annuity PW can be calculated. It is calculated by the formula PWA = Annuity * [(1 + iperiodic) ^ nperiods - 1] / [iperiodic * (1 + iperiodic) ^ nperiods]. Thus, the estimated PW of the net income made possible by the generator in the above example over the targeted six years would be calculated as
PWA = PWin = 120,000 * [(1 + 0.12) ^ 6 - 1] / [0.12 * (1 + 0.12) ^ 6] = 493,369 CFA.
Annuity calculations for uniform payments are much simpler than repeating the compounding or discounting formulas for the same cash stream, since they are just one equation rather than the sum of n number of equations for n periods. For non-uniform flows of recurring payments, or annuities with continuous compounding, consult a financial textbook such as Don Merino and Hans Lang's The Selection Process for Capital Projects [4], or a financial professional, or contact African Technology Forum Consulting for assistance as described above.
The future worth (FW) of a present amount of money is the same as compounding. It estimates what the present amount will equal at a specific future date given some particular rate of return. For a single payment of money, the formula is still (1 + iperiodic) ^ nperiods. For a uniform series of annuity payments, the future worth can be calculated by the formula FWA = Annuity * [(1 + iperiodic) ^ nperiods - 1] / iperiodic. Thus, the future worth of five annual net incomes of 30,000 rand for a South African investment option with an MARR of 8% can be calculated at the end of the fifth year as
FWA = 30,000 * [(1 + 0.08) ^ 5 - 1] / 0.08
= 30,000 * (1.08 ^ 5 - 1) / 0.08
= 30,000 * 5.8666 = R175,998
In another comparison of the time saved with annuity formulas, using the basic compounding formula itself would require the FW to be calculated as follows:
FW = 30,000 * (1 + 0.08) ^ 4 + 30,000 * (1 + 0.08) ^
3 + 30,000 * (1 + 0.08) ^ 2
+ 30,000 * (1 + 0.08) ^ 1 + 30,000
=
30,000 * [1.3604 + 1.2597 + 1.1664 + 1.08 + 1] = 30,000 * 5.8666 =
R175,998
Annual worth (AW) takes a series of cash flows, present worth values, and/or future worth values, and equates them to an equivalent annual cash flow. In this form, they can be compared amongst each other or to a given annuity. Annual worth is called annual cost when the value is a negative number.
The conversion of a present worth to an annual worth is computed as AW = PW * [i * (1 + i) ^ n] / [(1 + i) ^ n - 1]. It is the calculational inverse of the uniform series or annuity PW. This form of AW is known by the name "capital recovery". It denotes what uniform annual cash flow must be received in order to recover the equivalent power of a present sum of money. For example, with an MARR of 9%, in order to be as valuable as $100,000 USD today, a seven-year investment must net an annual income of at least:
AWCR = 100,000 * [0.09 * (1 + 0.09) ^ 7] /
[(1 + 0.09) ^ 7 -1] = 100,000 * 0.1987
= $19,869 USD
The form of AW that converts a future worth to an annual worth is called the "sinking fund" AW. What annual sum of money must be sunk in order to reach a particular future value of money given a particular rate or return? It is the calculational inverse of the uniform series FW and is calculated as AW = FW* i / [(1 + i) ^ n - 1]. Thus, with a rate of return of 9%, in order build an investment sum of $100,000 USD in seven years, an annuity at the end of each year must be paid equal to:
AWSF = 100,000 * 0.09 / [(1 + 0.09) ^ 7 -1] = 100,000 * 0.1087 = $10,870
In a similar vein to capital recovery, the common term "capitalized cost" is the present worth of a sum of outlays for a project that has both initial and periodic costs, such as annual maintenance. This can be calculated for projects by either summing the equivalent present worths of these outgoing cash flows for a long yet supposedly finite life of the project, or by assuming an infinite life for the project and simplifying the conversion of the annual costs. Although of course infinite life is technically not possible, the mathematics becomes simpler and the round off error due to the annualized present worth of payments 25-50 years down the line is relatively insignificant and well within the long-term margin of error introduced by external economic effects.
For finite life projects the capitalized cost (CC) can be calculated as CC = PWinitial + PWannuties. Let's analyze a local irrigation system in Botswana that will cost 3,000,000 pula to install in the first year, and an estimated P 100,000 to maintain each year after that. If the developers require an MARR of 8% for 30 years, the project's capitalized cost could be booked as
CCfinite = PWinitial + PWannuties
= 3,000,000 + 100,000 * [(1 + i) ^ n - 1] / [i * (1 + i) ^
n]
= 3,000,000 + 100,000 * [(1 + 0.08) ^ 30 - 1] / [0.08
* (1 + 0.08) ^ 30]
= 3,000,000 + 100,000 * [11.25778]
= P 4,125,778
If an infinite life is assumed, mathematical brevity conversely becomes possible. The present worth of the annual costs can be approximated by AW / i. This can be seen by taking the calculational limit of the above PWannuties formula as the number or periods n goes to infinity. Thus,
CCinfinite = PWinitial + AW / i
= 3,000,000 + 100,000 / 0.08
= 3,000,000 + 1,250,000
= P 4,250,000
Note the difference between CCfinite and CCinfinite is P 124,222, or just over one year's payments. In reality, it is highly unlikely that the annual maintenance costs for any multi-year project, let alone three decade's worth, can be known too precisely. The level of precision the infinite capitalized cost formula grants is not really a problem for long-term analyses. Which formula to use is more an issue of the method of bookkeeping the responsible parties intend to use and what tools are at hand. If the intended life of the irrigation system was 50 years, for instance, CCfinite would equal P 4,223,349, a difference of only P 26,652 or 0.63%. With the use of computer spreadsheets, the brevity of the infinite life formula doesn't add much distinct benefit. However, for manual bookkeeping with repeated hand calculations it can simplify the task greatly.
The internal rate of return (IRR) is used as a figure of merit once the net worth of a project has been determined or estimated. The IRR is calculated by finding the worths (present, future, or annual) of all the cash flows into a project and all the cash flows out, then setting their net difference equal to zero. The rate of return that allows for this difference to equal zero is the IRR.
When a future for-profit investment is being investigated, the IRR need only be calculated if the net present worth calculated at an established minimum attractive rate of return is positive or zero. If it is, the IRR will be equal to or greater than the established MARR. If not, the investment will not satisfy the MARR, and the unsatisfied investor will not choose to fund it. He or she will look for some alternative investment with better potential.
Although financial calculators and computer spreadsheets can automatically compute the IRR from a set of cash flows, typically it requires iterating the rates used in the PW formulas to generate the IRR value. Let us investigate a mining services operation in Jamaica that a Jamaican executive wants to propose to her corporate board. The firm is in a bit of a cash crunch as well as faces strong inflation. Facing these constraints, the board of directors requires any new operation to show an estimated MARR of 40% over five years before they choose to fund it rather than some other program or competing investment. The executive and her service development team feel that the initial outlay for the operation' s office space, equipment, and introductory marketing will be J$45,000,000. An initial market study suggests the service operation's annual revenues would be J$42,000,000 in present dollars. Including taxes, labor and all other costs, the annual net income is expected to be J$23,000,000. Not bad, but does it satisfy the firm's needs?
The net present worth is first calculated using the MARR as:
NPW = PWin - PWout = Annuity *
[(1 + i) ^ n - 1] / [i * (1 + i) ^ n] - PWout
= 23,000,000 * [(1 + 0.40) ^ 5 - 1] / [0.40 * (1 +
0.40) ^ 5] - 45,000,000
= 46,808,770 - 45,000,000 = J$1,808,770
Since the net present worth is positive, it will satisfy the firm's stated minimum needs. The board gives the operation the go-ahead, but still wants to know what the IRR looks like it's going to be. Since the positive NPW was relatively near zero for the MARR of 40%, the rate is first estimated to be fairly close, maybe 43%.
NPW = Annuity * [(1 + i) ^ n - 1] / [i
* (1 + i) ^ n] - PWout
= 23,000,000 * [(1 + 0.43) ^ 5 - 1] / [0.43 * (1 +
0.43) ^ 5] - 45,000,000
= - J$456,604
Closer, but not exact. Trying 42% results in
= 23,000,000 * [(1 + 0.42) ^ 5 - 1] / [0.42 * (1 +
0.42) ^ 5] - 45,000,000
= J$276,916
The NPW calculation has gotten even closer to zero, this time on the positive side. Thus, the estimated internal rate of return for this operation over these five years seems to be between 42-43%. Although compounding and discounting are mathematically exponential functions, common algebraic interpolation can be used to return a reasonably accurate answer between these two, for those who want better than two place results without further iterations.
IRR = 0.42 + (0 - 276,916) * (0.43-0.42) /
(-456,604 - 276,916)
= 0.4238 = 42.38%
Another figure of merit related to the IRR is the external rate of return (ERR). This is used in special circumstances when numerically, the cash flows over the lifetime of the project are very disruptive and reverse from net annual profits to net annual losses, or when large sums of cash need to be invested to replace and repair operations several times over the lifespan, or there are large end-of-project costs such as environmental reclamation. The standard IRR calculations may not return the proper rate results in these cases. For these circumstances, consult a financial textbook such as Don Merino and Hans Lang's The Selection Process for Capital Projects, or a financial professional, or contact African Technology Forum Consulting for assistance as described above.
While the present, future, and annual worths and the internal rate of return are excellent figures of merit to use for for-profit projects and investments where cash flows are being weighed for their value, obviously not all development projects are not based solely on their monetary impact. Governmental public projects and non-profit operations often require a way to judge the amount of benefit and social impact that their costs have procured or will procure. Once a goal is set in mind, the idea is to either justify the main proposal by ensuring it delivers more societal benefit than it brings societal costs, or to select from various proposals the one that has the highest benefits for its costs. Of course, these decisions need not only be judged using monetary values, but we will review how to generate useful fiscal metrics to help with the decision process.
The simplest version of the cost-to-benefit ratio, or benefit-to-cost ratio as it is also known, is B / C, where B is the total value of the benefits and C is the sum of the costs. Preferably, the ratio is greater than 1, but it can of course be used in a "least-of-all-evils" decision process when the individuals making the decisions are faced with a bad situation they are trying to contain and minimize with some proposed measure or measures.
For short-term projects, non-discounted cash flows are easy and accurate enough to use in the valuation of B and C, monetary destabilization and/or massive interest rates notwithstanding. For example, if after the floods of late 1999, a government agency in Mozambique looking to quickly rebuild one of three bridges to equal sized towns wanted to find a measure to judge how to use the scarce funds available for only one bridge, they could use the cost-to-benefit ratio.
If each town had 15,000 residents, all three towns had relatively equivalent socio-economic standards of living and health conditions, and the replacement costs for each of their bridges were maybe not equivalent but each by itself would make the single budget, what would be the best way to judge which town's bridge should be rebuilt? Let us imaging the three towns had three different economic outputs. Town #1 typically produced agricultural output valued at around 400,000,000 meticais, and its bridge to the main trade route would cost Me 150,000,000. Town #2 typically produced mineralogical output valued at around Me 450,000,000, and its bridge would require Me 175,000,000. Town #3 had some of the very few machine repair shops in that region and saved regional businesses about Me 350,000,000 per year by repairing industrial equipment instead of purchasing replacements on the foreign market. Its bridge would cost Me 125,000,000 to repair. Any of the three bridges could be repaired in two months. The ratios are as follows.
B/C
#1 = 400,000,000 / 150,000,000 = 2.667
B/C
#2 = 450,000,000 / 175,000,000 = 2.571
B/C
#3 = 350,000,000 / 125,000,000 = 2.800
Judging solely by cost-to-benefit ratio on these figures, Town #3 would be the one to have its bridge rebuilt. Note that in this example, the greatest estimated direct benefit would have accrued to the option with the worst ratio, #2. This does not mean that #3 is the wrong choice. When facing harsh circumstances with only scarce resources, it is best to always use a uniform metric to judge among various options. The Me 50,000,000 saved in costs by repairing bridge #3 instead could be used for some other worthwhile public project, preferably one with an equal or greater cost-to-benefit.
For projects that will last over several years, where compounding and discounting come into play, net equivalent worths of all the cash flows are generally required to make proper cost-to-benefit calculations. Since estimated societal benefits are very often thought of in terms of yearly figures and most government budgetary outlays are laid out as initial and/or annual costs, the use of equivalent annual worths is suggested. Present worths may also prove useful for cost-to-benefit calculations, as they can be compared to other fiscal challenges and opportunities at hand.
As can be seen, the cost-to-benefit ratio is a somewhat rough metric. Who is to say what one population's costs are versus another population's benefits? Have all secondary effects been accounted for? What about unintended consequences? One must keep in mind that no single metric, figure of merit, or decision will please everyone. Especially in least developed countries, it is extremely important to maximize the socio-economic impact of scarce resources by using objective metrics and decision processes to reach the fairest, most impartial conclusions.
When trying to use any of the above economic figures of merit to analyze a project, if you want to include the effects of uncertainties and risk, statistical sensitivity analyses and advanced risk assessment procedures coupled with the performance and decision matrices described herein should be used. One source of such information is Richard De Neufville's textbook Applied System Analysis: Engineering Planning and Technology Management. While dealing with such analyses in the assessment of technical projects, much of the text focuses on public projects such as infrastructure developments and investments. For more details and additional references, contact African Technology Forum Consulting for assistance as described above
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Michael
Tekletsion Berhan
African Technology Forum
Copyright
2000
Please note that African Technology Forum Consulting may be contacted to provide detailed examples of how to apply these tools to a particular situation. Visit www.africantechnologyforum.org, or write to us at africantech@att.net, mtberhan@alum.mit.edu, or mtberhan@att.net for any such assistance.
References
Clausing, Don P., Total Quality Development: A Step-by-Step Guide to World-Class Concurrent Engineering, American Society of Mechanical Engineers (ASME) Press, New York, 1994
Deming, W. Edward, Out of the Crisis, MIT Press, Cambridge, MA, 1986
De Neufville, Richard, Applied System Analysis: Engineering Planning and Technology Management, McGraw-Hill, New York, 1990
Merino, Donald N., and Lang, Hans J., The Selection Process for Capital Projects, John Wiley & Sons, New York, 1993
Samuelson, Paul A., and Nordhaus, William D., Economics, McGraw-Hill, New York, 1992
Slocum, Alexander H., Precision Machine Design, Prentice Hall, Englewood Cliffs, New Jersey, 1992